An Irnproved Method of Apertometry, 341 



will be found that they form a cone, the apex of which corresponds 

 with the optical centre of the plate. Structures lying anywhere 

 within this cone will therefore be visible to an observer looking 

 down the draw tube at the back lens of the objective, while struc- 

 tures lying outside this cone will be invisible. This makes the 

 setting of the images of the indices in coincidence with the 

 restricting aperture of the lens a difficult process. Ainslie (3) 

 described a similar difficulty in using Cheshire's apertometer. 

 Diagrams A and B (fig. 1) illustrate this difficulty. Placing the 

 indices so that their images are formed within the visible field does 

 not give benefit, as diagrams G and D (fig. 1) show. It is therefore 

 easily seen that according as one takes case (1) in which the tips, 

 or case (2) in which the intervals, are either seen or not seen, 

 so the measurement of the aperture will be too low or too high. A 

 method which allows the whole of the field (i.e. the region outside 

 the cone, corresponding to the limiting aperture of the objective) 

 to be visible removes the difficulty above described by allowing 

 the method of coincidence to be employed. This may be obtained 

 by reversing the direction of the light rays through the optical 

 system. For. this technique, therefore, the light source is placed 

 in the position of the eye-piece, and the rays of light descend 

 through the objective to spread out as a fan towards the periphery 

 of the apertometer plate. The numerical aperture is therefore 

 measured by setting the indices at the edge of the cone of illu- 

 mination proceeding from the objective, the edge being rendered 

 visible by frosting the curved side of the apertometer plate, or 

 preferably by observing the aerial image by means of a Eamsden 

 eye-piece. It will be seen at once that there are two advantages 

 to be gained by this technique : (1) the whole of the field is visible, 

 and therefore the method of coincidence may be employed ; (2) the 

 method can be used without modification for the examination of 

 condenser lens systems. Details of the technique will be given 

 later. 



Section 4. — Erkok in Apertometry due to the Incorrect 

 Determination of the Positions of the Indices in 

 Relationship to the Graduated Scale, and Inaccu- 

 racy IN THE Graduated Scale itself. 



Both these factors are entirely concerned with the construction 

 of the apparatus and its limitations. As manufactured by Zeiss 

 the instrument is imperfect, for the indices are so constructed that 

 the graduations are not closer than 0*05 N.A., and the sub- 

 division has to be done entirely by eye. This is made difficult by 

 the fact that only one side of the scale is visible (the other part 

 being hidden by the index itself). This point is clearly shown in 



